Interests of the group span a wide spectrum of homological algebra, group theory, quantum groups, representation theory, geometric number theory, noncommutative algebra, algebraic geometry, graph theory through to computer algebra and its applications in studying various problems in algebra and number theory. These areas are naturally related to coding theory.

Julian Abel studies many classes of combinatorial designs. He has found many new designs by powerful computer search, mainly using difference set methods. These designs form powerful bases for recursive constructions which establish the existence of important infinite classes of designs.
Examples of difficult problems in these areas are BIBDs with blocksize 7,8 or 9, V(11,t) vectors, perfect Mendelsohn designs, cyclic Whist designs, GBRDs over non-abelian groups and certain packing and covering designs.

Peter Brown has been working in the area of Number Theory, specifically on
Elliptic Curves and has recently been looking at some problems in Analytic
Number Theory.

Daniel Chan is interested in noncommutative algebra and algebraic geometry. His main research interest is in noncommutative algebraic geometry. This is a relatively new field, one important goal of which is to understand "geometrically", certain noncommutative algebras with homological properties similar to commutative algebras which arise naturally as coordinate rings of affine and projective varieties.
He has studied maximal orders on surfaces, noncommutative Grothendieck duality and coordinate rings associated to algebraic stacks.

Diana Combe studies finite groups, representations of primitive permutation groups and various areas of combinatorics. She is particularily interested in the actions of groups on graphs and directed graphs. In addition she is currently working
on combinatorial designs over finite groups, and on the labelling of graphs by abelian groups.

Peter Donovan works in representations of finite groups and associative algebras, with particular emphasis on connections with homological algebra. He also has interests in p-adic representation theory and algebraic aspects of the Hilbert problems. He is currently working on WW2 (Pacific) cryptanalysis.

Jie Du's interests lie in the representation theories on algebraic and quantum groups, finite groups of Lie type, finite dimensional algebras, and related topics. His recent work has concentrated mainly on the Ringel-Hall approach to quantum groups and q-Schur and generalised q-Schur algebras and their associated monomial and canonical basis theory. He is also interested in combinatorics arising from generalised symmetric groups, Kazhdan-Lusztig cells and representations of finite algebras.

James Franklin's mathematcial interests lie in unsupervised methods for data mining. He is also working on structuralist philosphy of mathematics. His most recent book, however, is on Australian philosophy, while a previous one studied the history of probability and evidence evaluation up to the seventeenth century.

Catherine Greenhill works in graph theory, particularly the theory of random graphs. This work involves a mixture of combinatorial and probabilistic arguments. She is also interested in the design and analysis of randomized algorithms for graphs and other combinatorial structures.

Mike Hirschhorn studies applications of q-series to problems in additive number theory. A greater part of his work is bound up in elucidating results due to Ramanujan.

David Hunt started his career in the area of finite group theory and made substantial contributions to the classification of finite simple groups, determining the character tables of some of the sporadic groups. He has also worked in problems in number theory, finite geometries and linear algebra. Much of his research has used the computer as a calculational tool.

Rod James works in the theory of p-groups. He has made significant use of the computer to calculate groups. During a recent visit to Queen Mary College, he worked on pro-p-groups with Leedham-Green. He is currently developing his interests in symbolic computation.

Dennis Trenerry has worked in the area of geometry of numbers, particularly on extremal problems with lattices.

Norman Wildberger 's interest in the theory of hypergroups has led him into description of various finite hypergroups. These have rather interesting algebraic properties and may be applied in the study of diophantine equations.